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ON THE COLOURS OF THICK PLATES.                    195
of diffraction. Furthermore, should the diffraction take place with a certain degree of regularity, as in the case of lycopodium seed, so as to exhibit rings or fringes in the aggregate effect of all the particles which send light into the eye in such a direction as to be brought to a given point on the retina, the diffraction rings and the interference rings are seen independent of each other*.
37. If 8 be the small angle of diffraction, 82 = of + y32, whence from (36) and the other equation which may be written down from symmetry,
l), + +/l'
hj       c     h)
Hence the loci of the points for which the angle of diffraction has given values form a system of concentric circles. Referring to (29), we see that the co-ordinates of the centre of the system are %v ylt so that the centre is situated in the point in which the mirror is cut by the line joining the eye and the image of the luminous point. This result might have been foreseen, since S vanishes only for the regularly refracted light, and this enters the eye only in the direction of the line joining the eye and the image. By introducing the co-ordinates gl9 yl, the equation (37) may be put under the form
+       (37).
hj ^     c    h)   ^    J
Since the diffraction becomes very sparing when the angle of diffraction becomes at all considerable, it follows that the interference rings are but weak at a considerable angular distance from the image of the luminous point. This agrees with observation. In the experiment in which a flame is placed in the centre of curvature of a concave mirror, and is then moved to one side, although the rings are symmetrical with respect to the flame and
* From some rough experiments which I have myself made with gauze stretched in front of a concave glass mirror, of which the surface was clean, I am inclined to think that the squarish rings observed by the Duke de Ohaulnes in the experiment with muslin, already mentioned, were due to a combination of the coloured rings of thick plates, and of the appearance produced by a cross-bar grating. If so, the independence of the two systems would have been rendered evident by slightly inclining the mirror, when the latter system would have had the image for its centre, whereas the former would have had for its centre a point situated midway between the luminous point and the image.